As shown by Gerardus 't Hooft, strong interactions of the standard model, QCD, possess a non-trivial vacuum structure that in principle permits violation of the combined symmetries of charge conjugation and parity, collectively known as CP. Together with effects generated by weak interactions, the effective periodic strong CP violating term, Θ, appears as a Standard Model input – its value is not predicted by the theory, but must be measured. However, large CP violating interactions originating from QCD would induce a large electric dipole moment (EDM) for the neutron. Experimental constraints on the currently unobserved EDM implies CP violation from QCD must be extremely tiny and thus Θ must itself be extremely small. Since a priori Θ could have any value between 0 and 2π, this presents a naturalness problem for the standard model. Why should this parameter find itself so close to 0? (Or, why should QCD find itself CP-preserving?) This question constitutes what is known as the strong CP problem.

One simple solution exists: if at least one of the quarks of the standard model is massless, Θ becomes unobservable. However, empirical evidence strongly suggests that none of the quarks are massless.

In 1977, Roberto Peccei and Helen Quinn postulated a more elegant solution to the strong CP problem, the Peccei–Quinn mechanism. The idea is to effectively promote Θ to a field. This is accomplished by adding a new global symmetry (called a Peccei–Quinn symmetry) that becomes spontaneously broken. This results in a new particle, as shown by Frank Wilczek and Steven Weinberg, that fills the role of Θ—naturally relaxing the CP violation parameter to zero. This hypothesized new particle is called the axion. (On a more technical note, the axion is the would-be Nambu–Goldstone boson that results from the spontaneously broken Peccei–Quinn symmetry. However, the non-trivial QCD vacuum effects (e.g. instantons) spoil the Peccei–Quinn symmetry explicitly and provide a small mass for the axion. Hence, the axion is actually a pseudo-Nambu–Goldstone boson.) The original Weinberg–Wilczek axion was ruled out. Current literature discusses the mechanism as the 'invisible axion' which has two forms: KSVZ [1][2] and DFSZ.[3][4]

It had been thought that the invisible axion solves the strong CP problem without being amenable to verification by experiment. Axion models choose coupling that it does not appear in any of the prior experiments. The very weakly coupled axion is also very light because axion couplings and mass are proportional. The situation changed when it was shown that a very light axion is overproduced in the early universe and therefore excluded.[5][6][7] The critical mass is of order 10−11 times the electron mass, where axions may account for the dark matter. The axion is thus a dark matter candidate as well as a solution to the strong CP problem. Furthermore, in 1983, Pierre Sikivie wrote down the modification of Maxwell's equations from a light stable axion [8] and showed axions can be detected on Earth by converting them to photons with a strong magnetic field, the principle of the ADMX. Solar axions may be converted to x-rays, as in CAST. Many experiments are searching laser light for signs of axions.[9]

Another technique is so called "light shining through walls",[13] where light passes through an intense magnetic field to convert photons into axions, that pass through metal. Experiments by BFRS and a team led by Rizzo ruled out an axion cause.[14] GammeV saw no events in a 2008 PRL. ALPS-I conducted similar runs,[15] setting new constraints in 2010; ALPS-II will run in 2014. OSQAR found no signal, limiting coupling[16] and will continue.

Several experiments search for astrophysical axions by the Primakoff effect, which converts axions to photons and vice versa in electromagnetic fields. Axions can be produced in the Sun's core when x-rays scatter in strong electric fields. The CAST solar telescope is underway, and has set limits on coupling to photons and electrons. ADMX searches the galactic dark matter halo[17] for resonant axions with a cold microwave cavity and has excluded optimistic axion models in the 1.9-3.53 μeV range.[18][19][20] It is amidst a series of upgrades and is taking new data, including at 4.9-6.2 µeV.

Resonance effects may be evident in Josephson junctions[21] from a supposed high flux of axions from the galactic halo with mass of 0.11 meV and density [22] compared to the implied dark matter density , indicating said axions would only partially compose dark matter.

Cryogenic detectors have searched for electron recoils. CDMS published in 2009 and EDELWEISS set coupling and mass limits in 2013. CUORE and XMASS also set limits on solar axions in 2013.

Axion-like bosons could have a signature in astrophysical settings. In particular, several recent works have proposed axion-like particles as a solution to the apparent transparency of the Universe to TeV photons.[23][24] It has also been demonstrated in a few recent works that, in the large magnetic fields threading the atmospheres of compact astrophysical objects (e.g., magnetars), photons will convert much more efficiently. This would in turn give rise to distinct absorption-like features in the spectra detectable by current telescopes.[25] A new promising means is looking for quasi-particle refraction in systems with strong magnetic gradients. In particular, the refraction will lead to beam splitting in the radio light curves of highly magnetized pulsars and allow much greater sensitivities than currently achievable.[26] The International Axion Observatory (IAXO) is a proposed fourth generation helioscope.[27]

Axions may have been detected through irregularities in X-ray emission due to interaction of the Earth's magnetic field with radiation streaming from the Sun. Studying 15 years of data by the European Space Agency's XMM-Newton observatory, a research group at Leicester University noticed a seasonal variation for which no conventional explanation could be found. One potential explanation for the variation, described as "plausible" by the senior author of the paper, was X-rays produced by axions from the Sun's core.[28]

A term analogous to the one that must be added to Maxwell's equations[29] also appears in recent theoretical models for topological insulators.[30] This term leads to several interesting predicted properties at the interface between topological and normal insulators.[31] In this situation the field θ describes something very different from its use in high-energy physics.[31] In 2013, Christian Beck suggested that axions might be detectable in Josephson junctions; and in 2014, he argued that a signature, consistent with a mass ~110μeV, had in fact been observed in several preexisting experiments.[32]

One theory of axions relevant to cosmology had predicted that they would have no electric charge, a very small mass in the range from 10−6 to 1 eV/c2, and very low interaction cross-sections for strong and weak forces. Because of their properties, axions would interact only minimally with ordinary matter. Axions would change to and from photons in magnetic fields.

If axions have low mass, thus preventing other decay modes, theories predict that the universe would be filled with a very cold Bose–Einstein condensate of primordial axions. Hence, axions could plausibly explain the dark matter problem of physical cosmology.[36] Observational studies are underway, but they are not yet sufficiently sensitive to probe the mass regions if they are the solution to the dark matter problem. High mass axions of the kind searched for by Jain and Singh (2007)[37] would not persist in the modern universe. Moreover, if axions exist, scatterings with other particles in the thermal bath of the early universe unavoidably produce a population of hot axions.[38]

Low mass axions could have additional structure at the galactic scale. As they continuously fell into a galaxy from the intergalactic medium, they would be denser in "caustic" rings, just as the stream of water in a continuously-flowing fountain is thicker at its peak.[39] The gravitational effects of these rings on galactic structure and rotation might then be observable.[40] Other cold dark matter theoretical candidates, such as WIMPs and MACHOs, could also form such rings, but because such candidates are fermionic and thus experience friction or scattering among themselves, the rings would be less pronounced.

Axions would also have stopped interaction with normal matter at a different moment than other more massive dark particles. The lingering effects of this difference could perhaps be calculated and observed astronomically. Axions may hold the key to the Solar corona heating problem.[41]